2002 Fiscal Year Final Research Report Summary

Study on Navier-Stokes equations and related nonlinear partial differential equations

Research Project

Project/Area Number	12640223
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Global analysis
Research Institution	Meiji University
Principal Investigator	MASUDA Kyuya Meiji University, Dept. of Science and Technology, Professor, 理工学部, 教授 (10090523)
Co-Investigator(Kenkyū-buntansha)	KATSURADA Masashi Meiji Univ., Dept. of Math., Assoc. Prof., 理工学部, 助教授 (80224484) KONNO Reiji Meiji Univ., Dept. of Math., Prof.(Lecturar 2002), 理工学部, 非常勤講師 MORIMOTO Hiroko Meiji Univ., Dept. of Math., Prof., 理工学部, 教授 (50061974) ISHIMURA Naoyuki Hitotsubashi Univ., Dept. of Econ., Assoc. Prof., 経済学部, 教授 (80212934) TANI Atsushi Keio Univ. Dept. of Math., Prof., 理工学部, 教授 (90118969)
Project Period (FY)	2000 – 2002
Keywords	Navier Stokes equations / Schroedinger operators / Minimal surfaces / Kuramoto-Syvashinsky equations / Stefan problem / general slip boundary condition / curvature equation / infinite channel
Research Abstract	Masuda succeeded in classifying completely the minimal surfaces of constant Gaussian curvature in two-dimensional complex form Morimoto showed the existence of solutions of two dimensional stationary Navier Stokes equations with general outlet boundary condition for some symmetric domain of channel type. Konno showed the non-existence of positive eigen-value for Schroedinger operator in the square integrable function space on unbounded domain. Ishimura and Nakamura found some important properties for the Kuramoto-Shivashinsky equations. Tani showed the existence of solutions of Navier-Stokes equations under the general slip boundary conditions.

Research Products
(25 results)

All Other

All Publications (25 results)

[Publications] Masuda, K., Kenmotsu, K.: "On minimalsurfaces of constant curvature in two-dimensional complex space form"J. reine angew. Math.. 523. 69-101 (2000)
- Description
  「研究成果報告書概要(和文)」より
[Publications] Morimoto, H., Fujita, H.: "On Stationary Navier-Stokes flows in 2D semi-infinite cchannel involving the general outflow condition"Ann. Univ. Ferra-Sez. VII. XLVI. 285-290 (2000)
- Description
  「研究成果報告書概要(和文)」より
[Publications] Konno, R.: "Square integarable solutions of Δμ+λμ=0 on noncompact maanifold"Tokyo Journal of Math.. 25. 285-294 (2002)
- Description
  「研究成果報告書概要(和文)」より
[Publications] Ishimura, N., Nakamura, M.: "A note on the nonexistence of nomonotone steady solutions of the Kuramoto-Syvashinsky equation"Ann. Univ. Ferra-Sez. VII. XLVI. 175-180 (2000)
- Description
  「研究成果報告書概要(和文)」より
[Publications] Tani, A., Itoh, H.: "The initial problem for the non-homogeneous Navier-Stokes equations general slip boundary condition"Proc. Royal Soc. Edinburgh. 130. (2000)
- Description
  「研究成果報告書概要(和文)」より
[Publications] Tani, A., Kusaka, Y.: "Classical slvability of the two phase Stefan problem in aa viscous incompressible fluid flow"Mathe. Models Methods in Appl. Sci.. 13. 365-391 (2002)
- Description
  「研究成果報告書概要(和文)」より
[Publications] Masuda, K.: "On minimal surfaces of constant curvature in two-dimensional complex space form"J. reine angew. Math.. 523. 69-101 (2000)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Morimoto, H. and Fujita, H.: "On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition"Ann. Univ.. Ferra-Sez.VII-Sc.Mat.XLVI. 285-290 (2000)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Morimoto, H. and Fujita, H.: "A remark on the existence of steady Navier-Stokes flow in 2D semi-channel involving outflow condition"Mathematica Bohemia. 126. 457-468 (2001)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Morimoto, H. and Fujita, H.: "A remark on the existence pf steady Navoier Stokes flows in a certain two-dimensional infinite channel"Tokyo J. Math.. 25. 307-321 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Konno, R.: "Square integrable solutions of Δu + λu = 0 on noncompact manifolds"Tokyo J. Maath.. 25. 285-294 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Ishimura, N. and Nakamura, M.: "A note on the nonexistence of monotonic steady solutions of the Kuramoto-Syvashinsky equation"Ann. Univ.. Ferra-Sez.VII-Sc.Mat.XLVI. 175-180 (2000)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Ishimura, N., Hamada, T., and Nakamura,M.: "Note on steady solutions of the Eguchi-Oki-Matsumura equation"Proc. Japan Academy. 76. 146-148 (2000)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Ishimura, N.: "Remarks on Third-order ODE's relevant to the Kuramoto- Shivashinsky equation"J. Differential Equations. 178. 466-477 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Ishimura, N., Aiki, T., Imai,H., Yamada,Y.: "Well-posedness of one-phase Stefan problems for sublinear heat equations"Nonlear Analysis. 51. 587-606 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Ishimura, N.: "Spiral solutions for a weakly anisotropic curvature flow equation"Advances in Math. Sci. Appl.. 12. 393-408 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., and Itoh: "The initial problem for the non-homogeneous Navier-Stokes equations with general slip boundary condition"Proc. Royal Soc. Edinburgh. 130A. 827-835 (2000)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., and Ogawa, M.: "Free boundary problem for an incompressible ideal fluid with surfaces tension"Math. Models Methods in Appl. Sci.. 12. 1725-1740 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., and Itoh, H.: "A boundary value problem for an infinite elastic strip with a semi-infinite crack"J. Elasticity. 66. 193-206 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., and Kusaka, Y.: "Classical solvability of the tgwo-phase Stefan problem in a viscous incompressible fluid flow"Math. Models Methods in Appl. Sci.. 13. 365-391 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., Kurokiba, M., and Tanaka, N.: "Existence of solutions for Eguchi-Oki-Matsumura equation and order-disorder transition in binary alloys"J. Math. Anal. Appl.. 272. 4448-4457 (2002)
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., and Tanaka, N.: "Surface waves for a compressible viscous flujid"J. Maath./Fluid Mech.. (to appear).
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., Itoh, S., and Tanaka, N.: "The initial value problem for the Navier-Stokes equations with general slip boundary condition in Hoelder spaces"J. Math. Fluid Mech.. (to appear).
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Tani, A., and Ogawa, M.: "Incompressible perfect fluid motion with free boudary of finite depth"Adv. Math. Sci. Appl.. (to appear).
- Description
  「研究成果報告書概要(欧文)」より
[Publications] Morimoto, H.: "Stationary Navier-Stokes flow in 2-dimensional Y-shape channel under general outflow condition, The Navier-Stokes equations: theory and numerical methods, ed. by R.Salvi"Marcel Dekker, Inc..
- Description
  「研究成果報告書概要(欧文)」より

2002 Fiscal Year Final Research Report Summary

Study on Navier-Stokes equations and related nonlinear partial differential equations

Principal Investigator

MASUDA Kyuya Meiji University, Dept. of Science and Technology, Professor, 理工学部, 教授 (10090523)

Research Products

[Publications] Masuda, K., Kenmotsu, K.: "On minimalsurfaces of constant curvature in two-dimensional complex space form"J. reine angew. Math.. 523. 69-101 (2000)

Description

[Publications] Morimoto, H., Fujita, H.: "On Stationary Navier-Stokes flows in 2D semi-infinite cchannel involving the general outflow condition"Ann. Univ. Ferra-Sez. VII. XLVI. 285-290 (2000)

Description

[Publications] Konno, R.: "Square integarable solutions of Δμ+λμ=0 on noncompact maanifold"Tokyo Journal of Math.. 25. 285-294 (2002)

Description

[Publications] Ishimura, N., Nakamura, M.: "A note on the nonexistence of nomonotone steady solutions of the Kuramoto-Syvashinsky equation"Ann. Univ. Ferra-Sez. VII. XLVI. 175-180 (2000)

Description

[Publications] Tani, A., Itoh, H.: "The initial problem for the non-homogeneous Navier-Stokes equations general slip boundary condition"Proc. Royal Soc. Edinburgh. 130. (2000)

Description

[Publications] Tani, A., Kusaka, Y.: "Classical slvability of the two phase Stefan problem in aa viscous incompressible fluid flow"Mathe. Models Methods in Appl. Sci.. 13. 365-391 (2002)

Description

[Publications] Masuda, K.: "On minimal surfaces of constant curvature in two-dimensional complex space form"J. reine angew. Math.. 523. 69-101 (2000)

Description

[Publications] Morimoto, H. and Fujita, H.: "On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition"Ann. Univ.. Ferra-Sez.VII-Sc.Mat.XLVI. 285-290 (2000)

Description

[Publications] Morimoto, H. and Fujita, H.: "A remark on the existence of steady Navier-Stokes flow in 2D semi-channel involving outflow condition"Mathematica Bohemia. 126. 457-468 (2001)

Description

[Publications] Morimoto, H. and Fujita, H.: "A remark on the existence pf steady Navoier Stokes flows in a certain two-dimensional infinite channel"Tokyo J. Math.. 25. 307-321 (2002)

Description

[Publications] Konno, R.: "Square integrable solutions of Δu + λu = 0 on noncompact manifolds"Tokyo J. Maath.. 25. 285-294 (2002)

Description

[Publications] Ishimura, N. and Nakamura, M.: "A note on the nonexistence of monotonic steady solutions of the Kuramoto-Syvashinsky equation"Ann. Univ.. Ferra-Sez.VII-Sc.Mat.XLVI. 175-180 (2000)

Description

[Publications] Ishimura, N., Hamada, T., and Nakamura,M.: "Note on steady solutions of the Eguchi-Oki-Matsumura equation"Proc. Japan Academy. 76. 146-148 (2000)

Description

[Publications] Ishimura, N.: "Remarks on Third-order ODE's relevant to the Kuramoto- Shivashinsky equation"J. Differential Equations. 178. 466-477 (2002)

Description

[Publications] Ishimura, N., Aiki, T., Imai,H., Yamada,Y.: "Well-posedness of one-phase Stefan problems for sublinear heat equations"Nonlear Analysis. 51. 587-606 (2002)

Description

[Publications] Ishimura, N.: "Spiral solutions for a weakly anisotropic curvature flow equation"Advances in Math. Sci. Appl.. 12. 393-408 (2002)

Description

[Publications] Tani, A., and Itoh: "The initial problem for the non-homogeneous Navier-Stokes equations with general slip boundary condition"Proc. Royal Soc. Edinburgh. 130A. 827-835 (2000)

Description

[Publications] Tani, A., and Ogawa, M.: "Free boundary problem for an incompressible ideal fluid with surfaces tension"Math. Models Methods in Appl. Sci.. 12. 1725-1740 (2002)

Description

[Publications] Tani, A., and Itoh, H.: "A boundary value problem for an infinite elastic strip with a semi-infinite crack"J. Elasticity. 66. 193-206 (2002)

Description

[Publications] Tani, A., and Kusaka, Y.: "Classical solvability of the tgwo-phase Stefan problem in a viscous incompressible fluid flow"Math. Models Methods in Appl. Sci.. 13. 365-391 (2002)

Description

[Publications] Tani, A., Kurokiba, M., and Tanaka, N.: "Existence of solutions for Eguchi-Oki-Matsumura equation and order-disorder transition in binary alloys"J. Math. Anal. Appl.. 272. 4448-4457 (2002)

Description

[Publications] Tani, A., and Tanaka, N.: "Surface waves for a compressible viscous flujid"J. Maath./Fluid Mech.. (to appear).

Description

[Publications] Tani, A., Itoh, S., and Tanaka, N.: "The initial value problem for the Navier-Stokes equations with general slip boundary condition in Hoelder spaces"J. Math. Fluid Mech.. (to appear).

Description

[Publications] Tani, A., and Ogawa, M.: "Incompressible perfect fluid motion with free boudary of finite depth"Adv. Math. Sci. Appl.. (to appear).

Description

[Publications] Morimoto, H.: "Stationary Navier-Stokes flow in 2-dimensional Y-shape channel under general outflow condition, The Navier-Stokes equations: theory and numerical methods, ed. by R.Salvi"Marcel Dekker, Inc..

Description